She was known as the British Chanel and her fans, including Joanna Lumley and dames Judi Dench and Maggie Smith, are as iconic and British as her label. But whereas Chanel has become one of the most powerful brands in the world, in just over a week Jean Muir will shut.

Jean Muir's closing sale began yesterday, marking the last time customers will be able to buy any clothes from this iconic British label. When the sale ends on April 20 so will the brand.

In scenes that brought back memories of the scrum at the new Primark flagship store in London last week, Jean Muir customers were queueing outside the shop well before the doors opened.

Inside, women, generally of the mid-century mark and older, politely if urgently dashed about the shop picking up Muir's iconic shift dresses, marked down from £395 to £200 and tweed jackets, down from £235 to £90. One was spotted making the dash from the dressing room to the clothing rails in just her underwear, and it was still before 11am.

"This really is the end of an era, and the end of something very important in British fashion," said Ann-Marie Allen, 53. "I've had things by her that are more than 15 years old and people still come up to me and say, gosh, that's a lovely dress."

When Muir launched her business in 1966 her simple shift dresses and beautifully cut but plain coats and evening gowns set the template for a minimalist look that defined British style before the pyrotechnics of punk took over. "There is something very British about her clothes in that they are understated and chic. I've been a fan for over 25 years," said shopper Elizabeth Morgan, clutching an armful of clothes.

There was also something of an old school British attitude in the brand's business approach. Muir refused to change her style and only since her death in 1995 has the company made tentative approaches to appeal to new, younger customers. She had a strong aversion to branding. Although the label name is still held in high esteem, the business has suffered in recent years.

With its lack of interest in celebrities - even though Joanna Lumley was Muir's first house model - and disinterest in trends it looked increasingly like a dusty relic in today's glitz obsessed fashion world, and the death of Muir herself hastened the company's end.

Some industry insiders have said that the company brought this on itself. Although Muir's death did affect the brand several investors have approached the family-owned company.

All these offers were rebuffed leading some to accuse the company of being an anachronism. Yet for a label that still insisted on holding its fashion shows in a discreet 19th century-style salon, with gilded chairs and polite applause, as opposed to the more modern approach of catwalks and paparazzi, this would probably be seen as a compliment.

When it was announced in January that the company was closing Muir's husband, Harry Leukert, who has run the business since her death, was bullish in defence of his decision: "It is sad but I think this is the way Jean would have wanted it. I have, of course, had other offers but I do not want Jean's name to fall into the wrong hands and be misused. That would be horrendous and she would have hated it. I believe there is a virtue in quitting while we are ahead and leaving her name untarnished."

Nicolas Steineke, managing director of Jean Muir, also pointed the blame at the general move in the fashion business to focusing on younger customers to the exclusion of everyone else.

"Our customers are older, and that has never been a problem for us as they are very loyal and know what they want. But department stores such as Harvey Nichols are now mostly interested in younger customers, and I really began to notice this over the past five years. When Harvey Nichols ended its business with us in 2005 our wholesale figures were very affected."

Customers yesterday focused on the clothes. Sarah Polden, with two pairs of trousers, a coat, four tops and a skirt, said: "My mother used to wear these clothes and I love them. It is very sad."

Best of British: life of a fashion icon

Jean Muir has often been called one of Britain's most iconic fashion designers but she herself would have recoiled from the description.

Partly this was because she generally shunned the kind of public adoration and bouquets most designers so assiduously court.

But mainly it was because she, with more than a touch of grandeur, insisted on the term "dressmaker", not "designer", which did not carry with it the former's suggestion of craft and skill.

Muir was born in London in 1922 and left school at 15 to go into fashion design. She designed some of Diana Rigg's wardrobe for The Avengers, including the famous catsuit. She launched the Jean Muir brand in 1966 and Joanna Lumley was her house model. "We all adored her, but we were also quite afraid of her," Lumley later said. Since then women as diverse as Lauren Bacall, Barbra Streisand, Bridget Riley and Judi Dench have all expressed their fondness for the label's high quality and understated elegance, which gave it a reputation for being "the British Chanel". Muir was awarded a CBE in 1984 and won the Museum of Costume's dress of the year award three times. She died in 1995.